Results 1  10
of
2,413
Alternatives to modelling sparsity in gene expression networks
"... Gene interaction networks are sparse: a particular gene is potentially regulated only by a small number of regulators; and also the number of possible regulators is reduced, compared to the total number of genes. Thus, in the process of estimating the network topology, this leads naturally to the co ..."
Abstract
 Add to MetaCart
. In this paper we examine some alternatives for introducing sparsity in a gene network model, from a Bayesian perspective. We focus mainly in time course gene expression measurements, but the techniques can be easily extended to crosssectional studies. In particular we use a dynamic Bayesian network setting
The Infinite Hidden Markov Model
 Machine Learning
, 2002
"... We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. Th ..."
Abstract

Cited by 637 (41 self)
 Add to MetaCart
We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data
On Model Selection Consistency of Lasso
, 2006
"... Sparsity or parsimony of statistical models is crucial for their proper interpretations, as in sciences and social sciences. Model selection is a commonly used method to find such models, but usually involves a computationally heavy combinatorial search. Lasso (Tibshirani, 1996) is now being used ..."
Abstract

Cited by 477 (20 self)
 Add to MetaCart
Sparsity or parsimony of statistical models is crucial for their proper interpretations, as in sciences and social sciences. Model selection is a commonly used method to find such models, but usually involves a computationally heavy combinatorial search. Lasso (Tibshirani, 1996) is now being
Regularization and variable selection via the Elastic Net.
 J. R. Stat. Soc. Ser. B
, 2005
"... Abstract We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, wher ..."
Abstract

Cited by 973 (11 self)
 Add to MetaCart
Abstract We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vect ..."
Abstract

Cited by 966 (5 self)
 Add to MetaCart
This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
Abstract

Cited by 935 (41 self)
 Add to MetaCart
and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done
Robust face recognition via sparse representation
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signa ..."
Abstract

Cited by 936 (40 self)
 Add to MetaCart
We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
Abstract

Cited by 427 (36 self)
 Add to MetaCart
A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Ranksparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
Abstract

Cited by 230 (21 self)
 Add to MetaCart
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable
Sparsity oracle inequalities for the lasso
 Electronic Journal of Statistics
"... Abstract: This paper studies oracle properties of ℓ1penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of nonzero components of the oracle vec ..."
Abstract

Cited by 171 (12 self)
 Add to MetaCart
Abstract: This paper studies oracle properties of ℓ1penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of nonzero components of the oracle
Results 1  10
of
2,413